eBook ISBN:  9780821876428 
Product Code:  CONM/55.2.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821876428 
Product Code:  CONM/55.2.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 55; 1986; 818 ppMSC: Primary 18
This volume presents a stateoftheart description of some of the exciting applications of algebraic \(K\)theory to other branches of mathematics, especially algebraic geometry and algebraic number theory. As the proceedings of a 1983 AMSIMSSIAM Joint Summer Research Conference, it includes current and important work by some of the best researchers in the field. The diverse scope includes the following topics: the matrix/vector bundle tradition of concrete computations for specific rings, the interaction with algebraic cycles, and the generalization of the regulator map for units in an algebraic number field to higher \(K\)groups of varieties over number fields.
Of particularly high research value are the ideas of Beilinsonon, which are presented here for the first time, the work of Merkurjev and Suslin relating \(K\)theory to the Brauer group (as reported by Merkurjev and Wadsworth), and the papers by Kato on algebraic cycles.
Directed towards mathematicians working in algebraic \(K\)theory, algebraic geometry, and algebraic number theory, this volume is also of interest to the algebraic topologist. The reader should be familiar with basic \(K\)theory and interested in its applications to other areas of mathematics.
This item is also available as part of a set: 
Table of Contents

Articles

P. E. Conner and Jürgen Hurrelbrink — A comparison theorem for the $2$rank of $K_2({\scr O})$ [ MR 862645 ]

Barry H. Dayton and Leslie G. Roberts — The Hilbert polynomial of a union of lines [ MR 862646 ]

Susan C. Geller — A note on injectivity of lower $K$groups for integral domains [ MR 862647 ]

David Goss — The theory of totally real function fields [ MR 862648 ]

J. S. Hsia — An application of algebraic $K$theory to sums of squares [ MR 862649 ]

Johannes Huebschmann — The homotopy type of $F\Psi ^q$. The complex and symplectic cases [ MR 862650 ]

J. Hurrelbrink and M. Kolster — On the $2$primary part of the BirchTate conjecture for cyclotomic fields [ MR 862651 ]

A. S. Merkurjev — $K_2$ of fields and the Brauer group [ MR 862652 ]

Robert Oliver — Torsion in homotopy equivalences of $S^1$bundles [ MR 862653 ]

Ulf Rehmann — Properties of the wild kernel of $K_2$ of global fields [ MR 862654 ]

Ulf Rehmann — Central extensions of ${\rm SL}_2$ over division rings and some metaplectic theorems [ MR 862655 ]

Victor Snaith — Constructing algebraic $K$theory elements from $K_1A$ [ MR 862656 ]

Victor Snaith — The equivariant second StiefelWhitney class, the characteristic classes of symmetric bilinear forms and orthogonal Galois representations [ MR 862657 ]

Siegfried Splitthoff — Finite presentability of Steinberg groups and related Chevalley groups [ MR 862658 ]

R. G. Swan and L. N. Vaserstein — On the absolute stable range of rings of continuous functions [ MR 862659 ]

Giovanni Taddei — Normalité des groupes élémentaires dans les groupes de Chevalley sur un anneau [ MR 862660 ]

Jerzy Urbanowicz — On the divisibility of generalized Bernoulli numbers [ MR 862661 ]

L. N. Vaserstein — On $K_1$theory of topological spaces [ MR 862662 ]

Adrian R. Wadsworth — Merkurjev’s elementary proof of Merkurjev’s theorem [ MR 862663 ]

J. Wagoner — The ${\bf Z}_p$regulator problem for $K_3$ [ MR 862664 ]

Charles A. Weibel — $K$theory of $1$dimensional schemes [ MR 862665 ]


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
This volume presents a stateoftheart description of some of the exciting applications of algebraic \(K\)theory to other branches of mathematics, especially algebraic geometry and algebraic number theory. As the proceedings of a 1983 AMSIMSSIAM Joint Summer Research Conference, it includes current and important work by some of the best researchers in the field. The diverse scope includes the following topics: the matrix/vector bundle tradition of concrete computations for specific rings, the interaction with algebraic cycles, and the generalization of the regulator map for units in an algebraic number field to higher \(K\)groups of varieties over number fields.
Of particularly high research value are the ideas of Beilinsonon, which are presented here for the first time, the work of Merkurjev and Suslin relating \(K\)theory to the Brauer group (as reported by Merkurjev and Wadsworth), and the papers by Kato on algebraic cycles.
Directed towards mathematicians working in algebraic \(K\)theory, algebraic geometry, and algebraic number theory, this volume is also of interest to the algebraic topologist. The reader should be familiar with basic \(K\)theory and interested in its applications to other areas of mathematics.

Articles

P. E. Conner and Jürgen Hurrelbrink — A comparison theorem for the $2$rank of $K_2({\scr O})$ [ MR 862645 ]

Barry H. Dayton and Leslie G. Roberts — The Hilbert polynomial of a union of lines [ MR 862646 ]

Susan C. Geller — A note on injectivity of lower $K$groups for integral domains [ MR 862647 ]

David Goss — The theory of totally real function fields [ MR 862648 ]

J. S. Hsia — An application of algebraic $K$theory to sums of squares [ MR 862649 ]

Johannes Huebschmann — The homotopy type of $F\Psi ^q$. The complex and symplectic cases [ MR 862650 ]

J. Hurrelbrink and M. Kolster — On the $2$primary part of the BirchTate conjecture for cyclotomic fields [ MR 862651 ]

A. S. Merkurjev — $K_2$ of fields and the Brauer group [ MR 862652 ]

Robert Oliver — Torsion in homotopy equivalences of $S^1$bundles [ MR 862653 ]

Ulf Rehmann — Properties of the wild kernel of $K_2$ of global fields [ MR 862654 ]

Ulf Rehmann — Central extensions of ${\rm SL}_2$ over division rings and some metaplectic theorems [ MR 862655 ]

Victor Snaith — Constructing algebraic $K$theory elements from $K_1A$ [ MR 862656 ]

Victor Snaith — The equivariant second StiefelWhitney class, the characteristic classes of symmetric bilinear forms and orthogonal Galois representations [ MR 862657 ]

Siegfried Splitthoff — Finite presentability of Steinberg groups and related Chevalley groups [ MR 862658 ]

R. G. Swan and L. N. Vaserstein — On the absolute stable range of rings of continuous functions [ MR 862659 ]

Giovanni Taddei — Normalité des groupes élémentaires dans les groupes de Chevalley sur un anneau [ MR 862660 ]

Jerzy Urbanowicz — On the divisibility of generalized Bernoulli numbers [ MR 862661 ]

L. N. Vaserstein — On $K_1$theory of topological spaces [ MR 862662 ]

Adrian R. Wadsworth — Merkurjev’s elementary proof of Merkurjev’s theorem [ MR 862663 ]

J. Wagoner — The ${\bf Z}_p$regulator problem for $K_3$ [ MR 862664 ]

Charles A. Weibel — $K$theory of $1$dimensional schemes [ MR 862665 ]